Question

Find the sum of the first eight terms of the geometric sequence whose first term is -2.5 and ratio is 2.

Answer 1

The sum of the first eight terms of the geometric sequence whose first term is -2.5 and ratio is 2 is: -637.5

The nth term of a geometric sequence is given mathematically as;

T(n) = ar^n

• where, a = first term of the geometric sequence.

• r = common ratio of the sequence

• and n = nth term of the sequence.

Therefore, the sum of the first 8 terms of the geometric sequence is;

• S(8) = a + ar + ar² + ar³ + ar⁴ + ar⁵ + ar⁶ + ar⁷.

In essence;

• since common ratio, r = 2

• and first term, a = -2.5

Therefore, we have;

• S(8) = -2.5(1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷)

• S(8) = -2.5(255)

S(8) = -637.5.

Therefore, the sum of the first eight terms of the geometric sequence whose first term is -2.5 and ratio is 2 is: -637.5

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